Deformation of singular fibers of genus two fibrations and small exotic symplectic 4-manifolds
We introduce the [Formula: see text]-nodal spherical deformation of certain singular fibers of genus two fibrations, and use such deformations to construct various examples of simply connected minimal symplectic [Formula: see text]-manifolds with small topology. More specifically, we construct new exotic minimal symplectic [Formula: see text]-manifolds homeomorphic but not diffeomorphic to [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using [Formula: see text]-nodal spherical deformations of certain singular fibers of genus [Formula: see text] fibrations.